Nonlocal anisotropic elastic shell model for vibrations of single-walled carbon nanotubes with arbitrary chirality

A nonlocal anisotropic elastic shell model is developed to study the effect of small scale on shell-like vibration of single-walled carbon nanotubes (SWCNTs) with arbitrary chirality. Anisotropic elastic shell model is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion are derived and analytical solution for the vibration of anisotropic SWCNTs is presented by using the Flügge shell theory and complex method. The suggested model is justified by a good agreement between the results given by the present model and available data in literature. Furthermore, the model is used to elucidate the effect of small scale on the vibration of zigzag, armchair and chiral SWCNTs. Our results show that small scale is essential for vibration of SWCNTs when the axial wave-length is not extremely long. Moreover, the results show that local model substantially overestimates vibrational frequencies of almost all modes.